非零方阵的一类加法分解  

An Additive Decomposition of Nonzero Square Matrices

作　　者：崔建 CUI Jian(School of Mathematics and Statistics,Anhui Normal University,Wuhu Anhui 241002,China)

机构地区：[1]安徽师范大学数学与统计学院,安徽芜湖241002

出　　处：《大学数学》2024年第2期100-105,共6页College Mathematics

基　　金：安徽省高等学校省级质量工程项目(2021jyxm0517,2021xxkc058)。

摘　　要：基于矩阵的相关性质,证明了数域上任意非零方阵均可分解为一个幂零阵与一个可逆阵之和,推进了已知相关结论.作为所得结果的应用,给出线性空间上线性变换的加法分解.Based on the related properties of square matrices,we prove that every nonzero square matrix over a number filed can express as the sum of a nilpotent matrix and an inverible matrix,which generalize some known results.As an application,the additive decompositions of linear transformations over a linear space are provided.

关 键 词：非零方阵 可逆阵 幂零阵 fine分解 

分 类 号：O151.2[理学—数学]